COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6300/8300
Title	Algebra I
Hours
Grading
Requisites
Catalog	Groups, Sylow's theorems, permutation groups, nilpotent and solvable groups, Abelian groups, rings, unique factorization domains, fields and field extensions, Galois theory, separable extensions of fields, modules, Noetherian and Artinian rings, tensor products, primitive and semisimple rings. Wedderburn-Artin theorem.	Groups, Sylow's theorems, permutation groups, nilpotent and solvable groups, Abelian groups, rings, unique factorization domains, and fields.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6310/8310
Title	Algebra II
Hours
Grading
Requisites
Catalog	Groups, Sylow’s theorems, permutation groups, nilpotent and solvable groups, Abelian groups, rings, unique factorization domains, fields and field extensions, Galois theory, separable extensions of fields, modules, Noetherian and Artinian rings, tensor products, primitive and semisimple rings. Wedderburn-Artin theorem.	Field extensions, Galois theory, modules, Noetherian and Artinian rings, tensor products, primitive rings, semisimple rings and modules, the Wedderburn-Artin theorem.
Reason	Presently, there is one description associated to both seme offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6320/8320
Title	Ring Theory I
Hours
Grading
Requisites
Catalog	Topics in ring theory chosen from among radical theory, rings of quotients, Goldie’s Theorem, chain conditions, dimensions of rings, module theory, topics in commutative rings, group rings, enveloping algebras, almost split sequences, PI-rings, division rings, self injective rings and ordered rings.	Radical theory, rings of quotients, Goldie's Theorem, chain conditions, dimensions of rings, module theory, topics in commutative rings.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6330/8330
Title	Ring Theory II
Hours
Grading
Requisites
Catalog	Topics in ring theory chosen from among radical theory, rings of quotients, Goldie’s Theorem, chain conditions, dimensions of rings, module theory, topics in commutative rings, group rings, enveloping algebras, almost split sequences, PI-rings, division rings, self injective rings and ordered rings.	Advanced topics in ring theory. Possible topics include group rings, enveloping algebras, almost split sequences, PI-rings, division rings, self-injective rings, and ordered rings.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6340/8340
Title	Group Theory I
Hours
Grading
Requisites
Catalog	Topics in group theory of wide applicability and of fundamental importance. Topics chosen from among presentations, free products amalgams, permutation groups, trees and graphs, solvability, nilpotence, linear representations, homological algebra, cohomology, character theory, classical groups, Lie rings, Sylow systems, Schur-Zassenhaus theorem, linear methods, local analysis, finiteness conditions.	Fundamental topics in group theory. Possible topics include free groups, presentations, free products and amalgams, permutation groups, abelian groups, nilpotent and solvable groups, subnormality, extensions, the Schur-Zassenhaus theorem, the transfer homomorphism, linear methods, local analysis.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6350/8350
Title	Group Theory II
Hours
Grading
Requisites
Catalog	Topics in group theory of wide applicability and of fundamental importance. Topics chosen from among presentations, free products amalgams, permutation groups, trees and graphs, solvability, nilpotence, linear representations, homological algebra, cohomology, character theory, classical groups, Lie rings, Sylow systems, Schur-Zassenhaus theorem, linear methods, local analysis, finiteness conditions.	Advanced topics in group theory. Possible topics include cohomology of groups, locally finite groups, character theory, modular representation theory, representation theory of symmetric and classical groups, finite simple groups, geometric group theory.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6400/8400
Title	Topology I
Hours
Grading
Requisites
Catalog	Topological spaces, continuous functions, compactness, product spaces. Tychonov theorem, quotient spaces, local compactness, homotopy, fundamental group, covering spaces, homology theory, excision, homological algebra, Brouwer fixed point theorem, cohomology, smooth manifolds, orientation, tangent bundles, Sard’s theorem, degree theory.	Topological spaces, continuous functions, compactness, product spaces, Tychonov’s theorem, quotient spaces, local compactness, homotopy theory, the fundamental group, covering spaces.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6410/8410
Title	Topology II
Hours
Grading
Requisites	MATH 5450 or equivalent	MATH 6400
Catalog	Topological spaces, continuous functions, compactness, product spaces, Tychonov theorem, quotient spaces, local compactness, homotopy, fundamental group, covering spaces, homology theory, excision, homological algebra, Brouwer fixed point theorem, cohomology, smooth manifolds, orientation, tangent bundles, Sard’s theorem, degree theory.	Homology theory, excision, homological algebra, the Brouwer fixed point theorem, cohomology, differential manifolds, orientation, tangent bundles, Sard’s theorem, degree theory.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations. Prerequisite error has been corrected.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6420/8420
Title	General Topology I
Hours
Grading
Requisites
Catalog	Categorical properties of and constructions in topological spaces, compactness, connectedness, dimension theory, metrization, compactification and proximity spaces, uniform spaces, completeness and completions, rings of continuous functions.	Categorical properties of and constructions in topological spaces, compactness, connectedness, dimension theory, metrization.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6430/8430
Title	General Topology II
Hours
Grading
Requisites	MATH 6400	MATH 6420
Catalog	Categorical properties of and constructions in topological spaces, compactness, connectedness, dimension theory, metrization, compactification and proximity spaces, uniform spaces, completeness and completions, rings of continuous functions.	Compactification and proximity spaces, uniform spaces, completeness and completions, rings of continuous functions.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations. Prerequisite error has been corrected.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6440/8440
Title	Differential Geometry I
Hours
Grading
Requisites
Catalog	Differentiable structures on manifolds, vector fields and flows, tensor bundles, distributions and Frobenius theorem, metric geometry, differential forms, Stokes theorem, Lie groups, connections on manifolds, geodesics, geometry of tangent bundle, curvature, torsion, exponential map, Rienammian geometry, geometry of submanifolds and submersion, relative Gauss-Bonnet theorem, homogeneous and symmetric spaces, topics in differential geometry.	Introduction to differential geometry. Topics include differentiable manifolds, vector fields, tensor bundles, the Frobenius theorem, Stokes' theorem, Lie groups.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6450/8450
Title	Differential Geometry II
Hours
Grading
Requisites	MATH 6410	MATH 6440
Catalog	Differentiable structures on manifolds, vector fields and flows, tensor bundles, distributions and Frobenius theorem, metric geometry, differential forms, Stokes theorem, Lie groups, connections on manifolds, geodesics, geometry of tangent bundle, curvature, torsion, exponential map, Rienammian geometry, geometry of submanifolds and submersion, relative Gauss-Bonnet theorem, homogeneous and symmetric spaces, topics in differential geometry.	Topics include connections on manifolds, Riemannian geometry, the Gauss-Bonnet theorem. Further topics may include: homogeneous and symmetric spaces, minimal surfaces, Morse theory, comparison theory, vector and principal bundles.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations. Prerequisite error has been corrected.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6460/8460
Title	Algebraic Topology I
Hours
Grading
Requisites
Catalog	Simplicial and cellular complexes, simplicial and cellular homology, universal coefficient theorem, Kunneth theorem, cohomology theories, cohomology operations, duality on manifolds, general homotopy theory, fibration nd cofibration, higher homotopy groups, weak homotopy equivalence, Hurewicz theorem, Eilenberg-Maclane spaces, classifying spaces, spectral sequences.	Simplicial and cellular complexes, simplicial and cellular homology, universal coefficient theorem, Künneth’s theorem, cohomology theories, cohomology operations, duality on manifolds.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6470/8470
Title	Algebraic Topology II
Hours
Grading
Requisites	MATH 6410	MATH 6460
Catalog	Simplicial and cellular complexes, simplicial and cellular homology, universal coefficient theorem, Kunneth theorem, cohomology theories, cohomology operations, duality on manifolds, general homotopy theory, fibration and cofibration, higher homotopy groups, weak homotopy equivalence, Hurewicz theorem, Eilenberg-Maclane spaces, classifying spaces, spectral sequences.	General homotopy theory, fibrations and cofibrations, higher homotopy groups, weak homotopy equivalence, Hurewicz’s theorem, Eilenberg-MacLane spaces, classifying spaces, spectral sequences.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations. Prerequisite error has been corrected.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6520/8520
Title	Dynamical Systems I
Hours
Grading
Requisites
Catalog	Flow-box theorem, Poincare maps, attractors, ω-limit sets, Lyapunov stability, invariant manifolds, Hamiltonian systems and symplectic manifolds, local bifurcations of vector fields homoclinic orbits, symmetries and integrals, integrable systems, symbolic dynamics chaos.	Topics include the flow-box theorem, Poincare maps, attractors, ω-limit sets, Lyapunov stability, invariant submanifolds, Hamiltonian systems and symplectic manifolds.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6530/8530
Title	Dynamical Systems II
Hours
Grading
Requisites	MATH 6500	MATH 6520
Catalog	Flow-box theorem, Poincare maps, attractors, w limit sets, Lyapunov stability, invariant manifolds, Hamiltonian systems and symplectic manifolds, local bifurcations of vector fields homoclinic orbits, symmetries and integrals, integrable systems, symbolic dynamics chaos.	Topics may include local bifurcations of vector fields, global stability, ergodic theorems, integrable systems, symbolic dynamics, chaos theory.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations. Prerequisite error has been corrected.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6540/8540
Title	Partial Differential Equations I
Hours
Grading
Requisites
Catalog	Sobolev spaces, Sobolev embedding theorem, distribution theory, weak solution to partial differential equations, existence, uniqueness and regularity of solutions, potential theory and harmonic functions, Hopf maximum principle, fundamental solutions and the parametrix, representation theorems, Cauchy-Kovalevskaya Theorem, topics in partial differential equations.	Possible topics may include: the Cauchy-Kovalevskaya Theorem, nonlinear partial differential equations of the first order, theory of Sobolev spaces, linear second order PDE's of elliptic, hyperbolic and parabolic type.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6550/8550
Title	Partial Differential Equations II
Hours
Grading
Requisites	MATH 6510	MATH 6540
Catalog	Sobolev spaces, Sobolev embedding theorem, distribution theory, weak solution to partial differential equations, existence, uniqueness and regularity of solutions, potential theory and harmonic functions, Hopf maximum principle, fundamental solutions and the parametrix, representation theorems, Cauchy-Kovalevskaya Theorem, topics in partial differential equations.	Selected topics in Partial Differential Equations of current interest emphasizing nonlinear theory. Possible topics may include: Minimal surfaces, applications of the Hopf maximum principle, free boundary value problems, harmonic maps, geometric evolution equations and the Navier-Stokes equation.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations. Prerequisite error has been corrected.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6720/8720
Title	Methods of Mathematical Physics I
Hours
Grading
Requisites
Catalog	Analytic functions, residues, method of steepest descent, complex differential equations, regular singularities, integral representation, special functions, real and complex vector spaces, matrix groups, Hilbert spaces, orthogonal polynomials, self-adjoint operators and eigenvalue problems, partial differential equations, coordinate transformations and separation of variables, boundary value problems, Green’s functions, integral equations, tensor analysis, metrics and curvature, calculus of variations, finite groups and group representations.	Analytic functions, residues, method of steepest descent, complex differential equations, regular singularities, integral representation, real and complex vector spaces, matrix groups, Hilbert spaces, coördinate transformations.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6730/8730
Title	Methods of Mathematical Physics II
Hours
Grading
Requisites		MATH 6720
Catalog	Analytic functions, residues, method of steepest descent, complex differential equations, regular singularities, integral representation, special functions, real and complex vector spaces, matrix groups, Hilbert spaces, orthogonal polynomials, self-adjoint operators and eigenvalue problems, partial differential equations, coordinate transformations and separation of variables, boundary value problems, Green’s functions, integral equations, tensor analysis, metrics and curvature, calculus of variations, finite groups and group representations.	Self-adjoint operators, special functions, orthogonal polynomials, partial differential equations and separation of variables, boundary value problems, Green’s functions, integral equations, tensor analysis, metrics and curvature, calculus of variations, finite groups and group representations.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations. Prerequisite error has been corrected.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6800/8800
Title	Real Analysis I
Hours
Grading
Requisites
Catalog	Completeness, connectedness and compactness in metric spaces, continuity and convergence, Stone-Weierstrass Theorem, Lebesgue measure and integration on the real line, convergence theorems, Egorov and Lusin theorem, derivatives, functions of bounded variation, Vitali covering theorem, absolutely continuous functions, Lebesgue-Stieltjes integration, Banach spaces, Lp-spaces, abstract measures, Radon-Nikodym Theorem, measures on locally compact Hausdorff spaces.	Completeness, connectedness and compactness in metric spaces, continuity and convergence, the Stone-Weierstrass Theorem, Lebesgue measure and integration on the real line, convergence theorems, Egorov’s and Lusin’s theorems, derivatives, functions of bounded variation.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6810/8810
Title	Real Analysis II
Hours
Grading
Requisites	MATH 5480 or equivalent	MATH 6800
Catalog	Completeness, connectedness and compactness in metric spaces, continuity and convergence, Stone-Weierstrass Theorem, Lebesgue measure and integration on the real line, convergence theorems, Egorov and Lusin theorem, derivatives, functions of bounded variation, Vitali covering theorem, absolutely continuous functions, Lebesgue-Stieltjes integration, Banach spaces, Lp-spaces, abstract measures, Radon-Nikodym Theorem, measures on locally compact Hausdorff spaces.	The Vitali covering theorem, absolutely continuous functions, Lebesgue-Stieltjes integration, the Riesz representation theorem, Banach spaces, Lp-spaces, abstract measures, the Radon-Nikodym theorem, measures on locally compact Hausdorff spaces.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations. Prerequisite error has been corrected.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6820/8820
Title	Functional Analysis I
Hours
Grading
Requisites
Catalog	Topological vector spaces, seminorms, Banach spaces, open mapping and closed graph theorem, convexity, weak topologies, Hahn-Banach theorem, Banach-Alaoglu theorems, duality, Lp spaces, Mackey-Ahrens Theorem, Banach algebras, spectra in Banach algebras, commutative Banach algebras, unbounded operators, spectral theorem for bounded and unbounded operators, topics in functional analysis.	Topics include Topological vector spaces, Banach spaces, convexity, the Hahn-Banach theorem, weak and strong topologies, Lp spaces and duality.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6830/8830
Title	Functional Analysis II
Hours
Grading
Requisites	MATH 6810	MAHT 6820
Catalog	Topological vector spaces, seminorms, Banach spaces, open mapping and closed graph theorem, convexity, weak topologies, Hahn-Banach theorem, Banach-Alaoglu theorems, duality, Lp spaces, Mackey-Ahrens Theorem, Banach algebras, spectra in Banach algebras, commutative Banach algebras, unbounded operators, spectral theorem for bounded and unbounded operators, topics in functional analysis.	Topics include the Mackey-Ahrens Theorem, Banach algebras, spectra in Banach algebras, commutative Banach algebras, unbounded operators, the spectral theorem, topics in functional analysis.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations. Prerequisite eror has been corrected.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2005.11
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6840/8840
Title	Complex Analysis I
Hours
Grading
Requisites
Catalog	Elementary analytic functions, complex integration, residue theorem and argument principle, sequences of analytic functions, Laurent expansions, entire functions, meromorphic functions, conformal mapping, Reimann mapping theorem, monodromy, algebraic functions, Riemann surfaces, elliptic and modular functions.	Elementary analytic functions, complex integration, the residue theorem, infinite sequences of analytic functions, Laurent expansions, entire functions.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations.
New Content?	no

COURSE MODIFICATION
Originator	Geoffrey Martin x2569 gmartin@math.utoledo.edu 2008./2
Department	Mathematics
	PRESENT	PROPOSED
Alpha code	MATH 6850/8850
Title	Complex Analysis II
Hours
Grading
Requisites	MATH 6800	MATH 6840
Catalog	Elementary analytic functions, complex integration, residue theorem and argument principle, sequences of analytic functions, Laurent expansions, entire functions, meromorphic functions, conformal mapping, Reimann mapping theorem, monodromy, algebraic functions, Riemann surfaces, elliptic and modular functions.	Meromorphic functions, conformal mapping, harmonic functions and the Dirichlet problem, the Riemann mapping theorem, monodromy, algebraic functions, Riemann surfaces, elliptic functions and the modular function.
Reason	Presently, there is one description associated to both semesters of the Department’s two semester graduate offerings. The change splits this description associating the first part of the description with the first semester and the second part with the second semester. There have been some changes of wording and condensations. Prerequisite error has been corrected.
New Content?	no